%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM021-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:17:50 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 9 unt; 2 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X0,X1] :
( ~ less(X2,X0)
| ~ less(X0,X1)
| less(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ equalish(add(successor(X0),X1),X2)
| less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',smaller_number) ).
fof(f9,axiom,
! [X0,X1] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',less_lemma) ).
fof(f10,axiom,
! [X0,X1] :
( ~ divides(X0,X1)
| less(X0,X1)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-2.ax',divides_only_less_or_equal) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ~ equalish(X1,X2)
| ~ equalish(X0,X1)
| equalish(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f16,axiom,
less(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_less_than_c) ).
fof(f17,axiom,
~ less(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_greater_equal_a) ).
fof(f18,negated_conjecture,
divides(c,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impossible_c_divides_a) ).
fof(f37,plain,
! [X0] :
( ~ less(c,X0)
| less(b,X0) ),
inference(resolution,[],[f7,f16]) ).
fof(f49,plain,
( less(c,a)
| equalish(c,a) ),
inference(resolution,[],[f10,f18]) ).
fof(f51,definition,
( spl0_1
<=> equalish(c,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f53,plain,
( equalish(c,a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f55,definition,
( spl0_2
<=> less(c,a) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f57,plain,
( less(c,a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f49,f55,f51]) ).
fof(f77,plain,
( less(b,a)
| ~ spl0_2 ),
inference(resolution,[],[f37,f57]) ).
fof(f78,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f77,f17]) ).
fof(f79,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f78]) ).
fof(f80,plain,
( ! [X0] :
( ~ equalish(X0,c)
| equalish(X0,a) )
| ~ spl0_1 ),
inference(resolution,[],[f53,f15]) ).
fof(f97,plain,
( ! [X0] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(c,X0)),X0),a)
| ~ less(X0,c) )
| ~ spl0_1 ),
inference(resolution,[],[f80,f9]) ).
fof(f855,plain,
( ! [X0] :
( ~ less(X0,c)
| less(X0,a) )
| ~ spl0_1 ),
inference(resolution,[],[f97,f8]) ).
fof(f863,plain,
( less(b,a)
| ~ spl0_1 ),
inference(resolution,[],[f855,f16]) ).
fof(f864,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f863,f17]) ).
fof(f865,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f864]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f58]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f79]) ).
cnf(s9,plain,
~ spl0_1,
inference(sat_conversion,[],[f865]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s2,s9]) ).
fof(f866,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM021-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 18:39:40 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.46 % (3249745)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (3249753)dis+10_1_sil=32000:sp=arity:random_seed=552479383:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (3249751)% WARNING: option uhcvi not known.
% 0.16/0.46 % (3249750)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1473810657_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (3249751)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4086228558:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (3249752)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2200346261:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (3249755)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=762169159:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (3249754)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2361237750:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (3249756)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3863164537:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % (3249753) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3249745-3249753"...
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % (3249753)...printing done.
% 0.16/0.46 % (3249753)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (3249753)------------------------------
% 0.16/0.46 % (3249753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (3249753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (3249753)CaDiCaL version: 2.1.3
% 0.16/0.46 % (3249753)Termination reason: Refutation
% 0.16/0.46 % (3249753)Time elapsed: 0.009 s
% 0.16/0.46 % (3249753)Peak memory usage: 12 MB
% 0.16/0.46 % (3249753)Instructions burned: 24 (million)
% 0.16/0.46 % (3249745)Success in time 0.047 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------